Between 1991 and 2007, Fuller Theological Seminary’s School on Intercultural Studies assembled a report on what drew Muslim converts to Christianity. The study of 750 people doesn’t claim scientific precision, but rather, a glimpse into what makes Jesus attractive to Muslims.
Guess what? No one was converted because of American tax policy, foreign policy, or social policy:

…respondents ranked the lifestyle of Christians as the most important influence in their decision to follow Christ. A North African former Sufi mystic noted with approval that there was no gap between the moral profession and the practice of Christians he saw. An Egyptian contrasted the love of a Christian group at an American university with the unloving treatment of Muslim students and faculty he encountered at a university in Medina. An Omani woman explained that Christians treat women as equals. Others noted loving Christian marriages. Some poor people said the expatriate Christian workers they knew had adopted, contrary to their expectations, a simple lifestyle, wearing local clothes and observing local customs of not eating pork, drinking alcohol, or touching those of the opposite sex. A Moroccan was even welcomed by his former Christian in-laws after he underwent a difficult divorce.
Many Muslims who faced violence at the hands of other Muslims did not see it in the Christians they knew (regrettably, of course, Christians have been guilty of interethnic strife elsewhere). Muslim-on-Muslim violence has led to considerable disillusionment for many Muslims, from those who survived the 1971 war between the Bengalis of East Pakistan and the Pathans, Sindis, and Punjabis of West Pakistan, to Arab and Berber tensions in North Africa, and to Arab herdsmen fighting black African farmers in Darfur.
The next most important influence was the power of God in answered prayers and healing. Like most of the factors that former Muslims list, experiences of God’s supernatural intervention often increase after Muslims decide to follow Christ.

What draws people to Jesus today is what has drawn people to him for 2,000 years – love; transformative and radical and authentic love that is the evidence of the Kingdom of Heaven on a dark earth.